MCAT ® PHYSICS REVIEW The Staff of Kaplan Contents How to Use this Book Introduction to the MCAT Part I: Review Chapter 1: Units and Kinematics Practice Questions Chapter 2: Newtonian Mechanics Practice Questions Chapter 3: Work Energy, and Momentum Practice Questions Chapter 4: Thermodynamics Practice Questions Chapter 5: Fluides and Solids Practice Questions Chapter 6: Electrostatics Practice Questions Chapter 7: Magnetism Practice Questions Chapter 8: DC and AC Circuits Practice Questions Chapter 9: Periodic Motion, Waves, and Sound Practice Questions Chapter 10: Light and Optics Practice Questions Chapter 11: Atomic Phenomena Practice Questions Chapter 12: Nuclear Phenomena Practice Questions Chapter 13: High-Yield Problem Solving Guide for Physics Part II: Practice Sections Practice Section Practice Section Practice Section Answers and Explanations Glossary Related Titles MCAT PHYSICS REVIEW KAPLAN’S EXPERT MCAT TEAM Kaplan has been preparing premeds for the MCAT for more than 40 years In the past 15 years alone, we’ve helped more than 400,000 students prepare for this important exam and improve their chances for medical school admission Marilyn Engle MCAT Master Teacher; Teacher Trainer; Kaplan National Teacher of the Year, 2006; Westwood Teacher of the Year, 2007; Westwood Trainer of the Year, 2007; Encino Trainer of the Year, 2005 John Michael Linick MCAT Teacher; Boulder Teacher of the Year, 2007; Summer Intensive Program Faculty Member Dr Glen Pearlstein MCAT Master Teacher; Teacher Trainer; Westwood Teacher of the Year, 2006 Matthew B Wilkinson MCAT Teacher; Teacher Trainer; Lone Star Trainer of the Year, 2007 Thanks to Jason Baserman, Jessica Brookman, Da Chang, John Cummins, David Elson, Jeff Koetje, Alex Macnow, Andrew Molloy, Josh Rohrig and Amjed Saffarini ABOUT SCIENTIFIC AMERICAN As the world’s premier science and technology magazine, and the oldest continuously published magazine in the United States, Scientific American is committed to bringing the most important developments in modern science, medicine, and technology to 3.5 million readers worldwide in an understandable, credible, and provocative format Founded in 1845 and on the “cutting edge” ever since, Scientific American boasts over 140 Nobel laureate authors, including Albert Einstein, Francis Crick, Stanley Prusiner, and Richard Axel Scientific American is a forum where scientific theories, and discoveries are explained to a broader audience Scientific American published its first foreign edition in 1890 and, in 1979, was the first Western magazine published in the People’s Republic of China Today, Scientific American is published in 17 foreign language editions with a total circulation of more than million worldwide Scientific American is also a leading online destination (www.ScientificAmerican.com) providing the latest science news and exclusive features to more than million unique visitors monthly The knowledge that fills our pages has the power to inspire, to spark new ideas, paradigms, and visions for the future As science races forward, Scientific American continues to cover the promising strides, inevitable setbacks and challenges, and new medical discoveries as they unfold How to Use this Book Kaplan MCAT Physics, along with the other four books in our MCAT Subject series, brings the Kaplan classroom experience to you—right in your home, at your convenience This book offers the same Kaplan content review, strategies, and practice that make Kaplan the #1 choice for MCAT prep All that’s missing is the teacher To guide you through this complex content, we’ve consulted our best MCAT instructors to call out Key Concept, to offer Bridge to better understanding of the material, and Mnemonic devices to assist in learning retention When you see these sidebars, you will know you’re getting the same insight and knowledge that classroom students receive in person Look for these as well as references to the Real World and MCAT expertise callouts throughout the book HIGH-YIELD MCAT REVIEW Following the content section, you will find a High-Yield Questions section These questions tackle the most frequently tested topics found on the MCAT For each type of problem, you will be provided with a stepwise technique for solving the question, as well as important directional points on how to solve it—specifically for the MCAT Our experts have again called out the Key Concepts , which show you which terms to review Next, the Takeaways box offers a concise summary of the problem-solving approach best used Things to Watch Out For points out any caveats to the approach discussed, which can lead to wrong answer choices Finally, Similar Questions allows you to practice the stepwise technique on analogous, open-ended questions STAR RATING The star rating is a Kaplan-exclusive system to help you focus your studies, using a 6-star scale Two factors are considered when determining the rating for each topic: the “learnability” of the topic—or how easy it is to master —and the frequency with which it appears on the MCAT exam For example, a topic that presents relatively little difficulty to master and appears with relatively high frequency on the MCAT would receive a higher star rating (e.g., or stars) than a topic which is very difficult to master and appears less frequently on the test The combination of these two factors represented by the star rating will help you prioritize and direct your MCAT studies We’re confident that this guide and our award-winning instructors can help you achieve your goals of MCAT success and admission to med school Good luck! Introduction to the MCAT The Medical College Admission Test, MCAT, is different from any other test you’ve encountered in your academic career It’s not like the knowledge-based exams from high school and college, where emphasis was on memorizing and regurgitating information Medical schools can assess your academic prowess by looking at your transcript The MCAT isn’t even like other standardized tests you may have taken, where the focus was on proving your general skills Medical schools use MCAT scores to assess whether you possess the foundation upon which to build a successful medical career Though you certainly need to know the content to well, the stress is on thought process, because the MCAT is above all else a critical thinking test That’s why it emphasizes reasoning, analytical thinking, reading comprehension, data analysis, writing, and problem-solving skills Though the MCAT places more weight on your thought process, you must have a strong grasp of the required core knowledge The MCAT may not be a perfect gauge of your abilities, but it is a relatively objective way to compare you with students from different backgrounds and undergraduate institutions The MCAT’s power comes from its use as an indicator of your abilities Good scores can open doors Your power comes from preparation and mindset because the key to MCAT success is knowing what you’re up against That’s where this section of this book comes in We’ll explain the philosophy behind the test, review the sections one by one, show you sample questions, share some of Kaplan’s proven methods, and clue you in to what the test makers are really after You’ll get a handle on the process, find a confident new perspective, and achieve your highest possible scores PASSAGE V 38 C The number of neutrons in a given isotope is determined by subtracting the number of protons in the nucleus from the number of nucleons, N = A - Z = 236 − 92 = 144 neutrons for a Not knowing that the question refers to the intermediate product would lead us to the other answer choices 39 C The amount of untouched naturally occurring weapons-grade uranium, , has decreased due to radioactivity by more than a factor of two, because the age of the Earth is more than half-life of this isotope Half-life is defined as the time it takes for half of the original amount a given radioactive isotope to decay 40 C The amount of a radioactive sample decreases exponentially Here, 11,260 years happens to be equal to two times 5,630 years, which is the for half-life 6C14 This means that one quarter of the original sample will remain after two half-lives One must refer to the passage for specific values 41 B The radioactive decay rate, also called the activity, decreases exponentially, just like the amount of a radioactive sample After one half-life, 5,630 years, the decay rate will be half of the initial value Refer to the passage for the values needed to carry out this problem 42 B ß decay is defined as the emission of an electron by a nucleus The figure shows this sort of emission, so it clearly represents a ß decay An anti-neutrino is also emitted in the decay, and has no mass or charge 43 D A neutron is converted into a proton, an electron, and an anti-neutrino 44 C Assuming 15 decays per minute per gram of carbon, a 100-gram sample would initially have a decay rate of 1,500 decays per minute when the organism dies If the decay rate is currently 187.5 decays per minute, that means that the organism died three half-lives ago PASSAGE VI 45 D Critical angles are only a consideration when light moves from a medium of high index of refraction into a medium of low index, relative to the first In outer space, the originating medium is a vacuum for which the index of refraction is infinity Had we used the equation for critical angles, sin θ c = n2/n1 = nglass /nvacuum, we would have gotten a number greater than (and the sine of an angle can never be greater than 1) This might have tempted us to choose (A) over (D) Had we flipped this, however, we would have seen that sin θ c was 0.5 and that θc was 30° Remember, though, that since the question tells us that a laser beam in space was pointed toward the glass block, that this critical angle would refer to light inside the block, crossing the boundary into the vacuum of space (D) is indeed the answer, as no critical angle would exist Total internal reflection cannot occur 46 C Although the lenses touched, this should be considered a multiple-lens system For such a system, there is one very helpful equation from our arsenal of optics equations: 1/f = 1/f + 1/ f2 The question is mathematically quite simple after we realize these few points Our objective is f, because we have f1 and f2 We have the focal length of the original, 57.5 m 10 percent of this is 5.75, or 23/4 The inverse of that is 4/23 and we double this to get 8/23 Setting this equal to 1/f, we find that f is about 2.9 m Mathematical errors along the way or assuming the focal length of one lens to be sufficient would produce (D) Using 8/23 instead would produce 0.3 m (B) Using negative focal lengths would give us the negative of our correct answer, and this is incorrect when using converging lenses 47 B The relationship between wavelength and frequency is inverse; a wave with high frequency must have small wavelength and vice versa Though we might not know the entire order of the visible spectrum, we can still make some headway with these options If we know that wavelength decreases in the order of ROYGBIV we know that red has the longest wavelength of the visible spectrum Also recall that infrared light falls right next to red visible light and that it has higher wavelength On the other side, ultraviolet light lays next to violet light, which has a smaller wavelength You should be familiar with the general fact that X-rays are very high-energy waves The relationship between energy and frequencyis direct ( E = hf) and thus between energy and wavelength, it is inverse We can then say that the order of these waves, from smallest wavelength, is X-rays, UV, visible, then infrared light 48 D This question is a bit time consuming because it requires you to sketch some graphs Items II and IV are correct We know that for an object starting from rest and moving with constant acceleration, a = v/t Because Graph A reflects speed versus time, we know that the slope of the line is acceleration We’re told that acceleration is constant, so the line representing it will be straight However, we know that acceleration is not zero and so item I is incorrect Next, for distance, we can look to one of our one-dimensional motion equations: x − x0 = v 0t + ½ at2 The equation shows us that the relationship between distance and time is parabolic and symmetrical about the x-axis Distance is constantly decreasing We know, then, that item IV is correct 49 C Only item IV is incorrect Acceleration is the same for all falling objects Even though acceleration may be different at this height above the Earth’s surface, it will affect the two objects identically (as long as we can neglect air resistance) Item I is correct Next, v = at tells us that the speed of a falling object starting from rest is proportional to the acceleration and the time of fall These values have nothing to with the mass of the object Therefore, item II is incorrect Items III and IV differentiate potential energy Recalling the formula PE = mgh, in this case g and h are identical for the two objects, though mass is of some consequence Because potential energy and mass are proportional, the hammer—with greater mass—will have greater potential energy 50 D There are several ways to go about this problem One is to make a graph of the known values With a graph indicating velocity versus time, we could find the area under the graph Another way is to use the average speed (we can only this because acceleration is constant) We simply multiply the average speed by the time traveled To get the average speed, we add the initial speed to the final speed and divide by We’re told the speed has decreased by 10 percent, but what was the speed to begin with? Such a speed was provided in the passage and we can quickly refer back for this number: 7,500 m/s When this decreases by 10 percent, we have a new speed of 6,750 m/s This would give us that the average speed is 7,125 m/s, or simply a reduction of percent overall Stopping here would produce (B), which is an incorrect answer Multiplying this by seconds, we get that the distance covered is 35,625 m Dividing would produce (A) Using 6,750 m/s here instead would produce (C) 51 D While we might be relieved that the passage provides the speed of the telescope, this is not the speed with which we’re concerned In fact, this is only the initial horizontal velocity Rather, an object falls under the influence of gravity and its descent is not affected by this value We use the equation x-xo = vot +½at2 We not completely dismiss the passage, because we need Hubble’s height, 600 km Plugging this in, we get 600,000 m = (0 m/s)( t) +½(10 m/s2) (t2), and t2 = 120,000 S Though it would be difficult to know the value of t right off the bat, it is safe at this point to choose from the given answer choices The only value which comes close is 346 s, or minutes and 46 seconds Failing to convert km to m would have given you (A), about 11 seconds Of course, carrying units would prevent that mistake Using a = v/t would have given you 60 s (1 min), choice (B) 52 C The concave spherical mirror identified in the passage will be of most help here Though the equation 1/0 + 1/i = 1/f might guide you here, you should also be able to visualize the actual rays that produce the images whose distances and heights we calculate This question tests that ability First, we must realize that incident rays parallel to the axis of a concave mirror will converge to the focal point This will be the case for all rays that travel parallel If we imagined that a certain source of light was producing these rays, a ray which goes through the focal point would reflect back through the focal point A ray which travels straight to the center of curvature will return back at the same angle that the original ray had made, with the incident ray above the horizontal and refracted ray below the horizontal A ray would not travel normal, or perpendicular, to the axis, so (A) is out Due to the curvature of the mirror, it would not travel parallel This would happen with a plane mirror (B) is out as well (C) is the focal length of 57.6 m, from the passage, and (D) uses f as a value Knowing that all parallel rays will converge at the focus, we choose (C) over (D) Glossary Absolute pressure The actual pressure Acceleration A vector quantity; the time-rate of change in velocity Adiabatic A process in which heat flows neither into nor out of a system Alternating current A current that changes directions periodically, often in a sinusoidal fashion Alpha (α) particle A helium nucleus Amplitude The maximum displacement from an equilibrium position; the magnitude of the maximum disturbance in a wave Antinode Points of maximum amplitude in a standing wave Archimedes’ principle A body immersed in fluid experiences an upward buoyant force equal to the weight of the displaced fluid Atomic mass The mass of an atom of an element in amu (atomic mass units) Atomic mass unit (amu) One-twelfth (1/12) of the mass of the carbon-12 atom Atomic number The number of protons in a nucleus; this number characterizes each element Atomic weight The average mass of an element’s atoms—a weighted average of the different isotopes, weighted according to each isotope’s naturally occurring abundance Beats The sound produced by the alternating constructive and destructive interference between sound waves of slightly different frequencies Beta (β) particle An electron; usually refers to one emitted in radioactive beta decay Binding energy The energy required to separate an electron from an atom or to completely separate the protons and neutrons in a nucleus Buoyant force The upward force felt by a body partially or wholly submerged in a fluid that is equal to the weight of the fluid that the submerged body has displaced (see also Archimedes’ principle) Capacitance A measure of the ability of a capacitor to store charge; the absolute value of the magnitude of the charge on one plate divided by the potential difference between the plates Capacitor Two conducting surfaces that store equal and opposite charges when connected to a voltage source Center of gravity A point such that the entire force of gravity can be thought of as acting at that point If the acceleration of gravity is constant, then the center of gravity and the center of mass are at the same point Center of mass The point that acts as if the entire mass was concentrated at that point Centripetal acceleration The acceleration of an object that travels in a circle at a constant speed The magnitude of the acceleration is equal to the velocity squared divided by the radius of the circle It is always directed towards the center of the circle (If the velocity is not constant, there is a second component of acceleration tangent to the circle.) Centripetal force The force responsible for the centripetal acceleration Its magnitude is equal to the product of the mass and square of the velocity divided by the radius of the circle Like centripetal acceleration, it is always directed towards the center of the circle, provided that the velocity of the object is constant Conductor A material, such as metal, in which electrons can move relatively freely Conservative force A force is conservative if the work done on a particle in any round trip is zero, or if the amount of work done by moving a particle from one position to another is independent of the path taken Convection The transfer of heat through the bulk motion of the heated material Critical angle The critical angle is the angle of incidence such that the refracted angle is 90° when light is going from a medium having a higher index of refraction into a medium having a lower index of refraction Decay constant The proportionality constant between the rate at which radioactive nuclei decay and the number of radioactive nuclei remaining Decibel A unit of sound level Density Mass per unit volume Dielectric A nonconducting material often placed between plates of a capacitor to increase the capacitance Diffraction The bending of waves as a result of passing through a slit; the bending of waves around an obstacle Diopter A measure of a lens’s power, defined as the inverse of the focal length in meters Dipole moment A vector whose magnitude is the product of the charge of the dipole and the distance separating the two charges For physicists, the vector points from the negative charge towards the positive charge (chemists sometimes use the reverse direction) Dispersion The variation of wave-speed with frequency in a medium; the separation of visible light into its constituent colors (for example, by a prism) as a result of this variation Displacement A vector quantity; the straight-line distance and direction going from some initial position to some final position Doppler effect The change in frequency of a wave as a result of the motion of the source and/or observer along the line joining them Electric current The net charge per unit time passing through a given cross section; by convention, the direction is that in which positive charge would flow Electric dipole Two equal and opposite electric charges separated by a small distance Electric field The electrical force on a stationary positive test charge divided by the charge Electric potential The work needed to move a positive test charge from infinity to a given point in an electric field divided by the charge The electric potential can also be considered the electric potential energy per unit charge Electromagnetic wave A transverse wave of changing electric and magnetic fields Electromagnetic spectrum The full range in frequency and wavelength of all electromagnetic waves Electromotive force The voltage across the terminals of a cell or battery when no current is flowing Energy The ability to work Entropy The measure of a system’s disorder Equilibrium See Rotational equilibrium, Translational equilibrium Excited state An atom in which an electron occupies an energy state above the minimum energy state or ground state; a nucleus that is in an energy level above its ground state energy level Field line A technique used to better visualize electric or magnetic field patterns The tangent to a field line at any point is the direction of the field itself at that point The more field lines per unit area, the greater the magnitude of the field Fission The splitting of a heavy nucleus into two or more lighter nuclei accompanied by the release of energy Fluorescence A process in which certain substances emit visible light when excited by other radiation, usually ultraviolet radiation Focal length The distance from a mirror or lens to the focal point Focal point The point at which rays of light parallel to the optic axis converge, or appear to diverge from, when reflected from a mirror or refracted by a lens Frequency The number of cycles per second; the number of wavelengths of a traveling sinusoidal wave passing a fixed point per second Friction The force that two surfaces in contact exert on each other in a direction parallel to their surfaces and opposite to their motion Fundamental frequency The lowest frequency at which a standing wave can be produced on or in a body Fusion The combining of lighter nuclei into a heavier nucleus accompanied by the release of energy Gamma (γ) radiation High-energy photons, often emitted in radioactive decay Gauge pressure The difference between the absolute pressure and atmospheric pressure Gravity A fundamental force of attraction between all matter Its magnitude is directly proportional to the product of the masses and inversely proportional to the square of the distance between their centers Ground state The lowest energy state of an atom or nucleus Half-life The time in which one-half of the radioactive nuclei that were originally present decay Heat The energy that is transferred between two objects as a result of a difference in temperature Heat conduction The transfer of heat energy through a body without bulk motion of the material within the body Impulse A vector quantity; the force acting on an object multiplied by the time the force acts; also the change of momentum of an object Index of refraction The ratio of the speed of light in a vacuum to the speed of light in a medium Inertia An object’s resistance to a change in its motion when a force is applied Insulator A material in which electrons not move freely Intensity The average rate per unit area of energy transported by a wave across a perpendicular surface Interference The combined effects of two waves— constructive when the waves are in phase, destructive when they are out of phase Isobaric A process in which the pressure of a system remains constant Isothermal A process in which the temperature of a system remains constant Isotopes Atoms of a given element whose nuclei have the same number of protons but a different number of neutrons and, therefore, have the same atomic number but different mass numbers Kinetic energy The energy a body has as a result of its motion Line of force See Field line Longitudinal wave A wave in which the oscillation is parallel to the direction of propagation Magnetic field A magnetic property associated with a point; the maximum magnetic force on a moving positive test charge divided by its charge and its velocity Mass A measure of a body’s inertia Mass defect The difference between the sum of the masses of neutrons and protons forming a nucleus and the mass of that nucleus Mass number The total number of protons and neutrons in the nucleus of an atom Momentum A vector quantity; mass times velocity Node Points where the displacement of a standing wave remains zero at all times Normal In optics, the normal is a line drawn perpendicular to the boundary between two media Normal force The force that two surfaces in contact exert on each other in a direction perpendicular (normal) to the area of contact Nucleon A member of the nucleus, either proton or neutron Pascal’s principle The pressure applied to an enclosed fluid is transmitted undiminished to every portion of the fluid and to the walls of the vessel containing the fluid Period The time necessary to complete one cycle Polarized light Light that has all of its electric field vectors parallel Positron Antiparticle of an electron; it has the same mass as an electron and a charge that is equal to the charge of an electron in magnitude but opposite in sign (i.e., positive) Potential difference The difference of electrical potential between two distinct points; the work needed to move a unit positive charge between two points Potential energy The energy that a body has as a result of its position when a conservative force is acting on it Power The time-rate at which work is done or energy is transferred Pressure Force per unit area Quantum A discrete bundle of energy, such as a photon (particle of light) Radiation The transfer of energy by electromagnetic waves Resonance The phenomena in which an oscillatory system absorbs, with extremely high efficiency, the energy transmitted by an external oscillatory force having a frequency equal to one of the system’s natural frequencies Reflection The change in direction of a wave at the boundary of a medium when the wave remains in the medium Refraction The change in direction of a wave as it passes obliquely through a boundary from one medium to another Resistance A characteristic property of a conductor, which measures the opposition to current flowing through it; the ratio of the voltage applied to a conductor and the current that results Resistivity A measure of the intrinsic resistance of a material independent of its shape or size rms current The maximum current divided by the square root of 2; used to measure the current in an AC circuit in lieu of the average current, which is zero Rotation The turning of an extended body about an axis or center; change in orientation Rotational equilibrium The condition where the sum of the torques acting on a body is zero; also called the equilibrium Scalar A quantity that has a magnitude but not a direction; an ordinary number Simple harmonic motion second condition of Periodic motion about an equilibrium position resulting from a linear restoring force Sound level Ten times the logarithmic ratio of the intensity of a given sound to the intensity of the faintest sound that can be heard by humans Specific gravity The ratio of the density of a substance to the density of water Specific heat The number of calories needed to raise the temperature of one gram of a substance by 1°C Speed A scalar quantity; the instantaneous rate at which distance is being covered by a moving object Standing wave A wave with a displacement that appears fixed in space and time It can be produced when two waves of the same frequency, amplitude, and speed travel in opposite directions Superposition principle The resulting displacement of a medium at a point where two or more waves meet is the algebraic sum of the individual displacements of each wave at that point Thermal expansion The change in an object’s size with a change in temperature In general, objects expand as the temperature increases Torque The magnitude of the force acting on a body times the perpendicular distance between the direction of the force and the point of rotation Translation Motion through space without a change in orientation Translational equilibrium The condition in which the sum of the forces acting on a body is zero, also called the equilibrium Transverse wave A wave in which the oscillation is perpendicular to the direction of propagation Vector A quantity that has both magnitude and direction first condition of Velocity A vector quantity whose magnitude is speed and whose direction is the direction of motion Viscosity A fluid’s internal resistance to flow Wavelength The distance between two corresponding points in successive cycles of a sinusoidal wave; the distance from one crest to the next Weight The force of gravity on an object, not to be confused with mass Work A scalar quantity; the force acting on an object times the distance the object moves times cos angle between the force and the direction of motion θ, where θ is the Related Titles Kaplan MCAT Biology Review * Kaplan MCAT General Chemistry Review * Kaplan MCAT Organic Chemistry Review * Kaplan MCAT Physics Review * Kaplan MCAT Verbal Reasoning and Writing Review * Kaplan MCAT Premier Kaplan MCAT 45 MCAT Flashcards Get into Medical School* Med School Rx* Applications for iPhone MCAT Comprehensive Flashcards MCAT Review Notes * Also available in eBook format MCAT® is a registered trademark of the American Association of Medical Colleges, which neither sponsors nor endorses this product This publication is designed to provide accurate and authoritative information in regard to the subject matter covered It is sold with the understanding that the publisher is not engaged in rendering legal, accounting, or other professional service If legal advice or other expert assistance is required, the services of a competent professional should be sought © 2010 by Kaplan, Inc All rights reserved under International and Pan-American Copyright Conventions By payment of the required fees, you have been granted the non-exclusive, non-transferable right to access and read the text of this e-book on screen No part of this text may be reproduced, transmitted, downloaded, decompiled, reverse engineered, or stored in or introduced into any information storage and retrieval system, in any form or by any means, whether electronic or mechanical, now known or hereinafter invented, without the express written permission of the publisher eISBN : 978-1-60714-942-2 Published by Kaplan Publishing, a division of Kaplan, Inc Liberty Plaza, 24th Floor New York, NY 10006 10 Kaplan Publishing books are available at special quantity discounts to use for sales promotions, employee premiums, or educational purposes For more information or to purchase books, please call the Simon & Schuster special sales department at 866-506-1949